A failure by the U.S. to raise its debt limit would be "absolutely absurd" and risk the credibility of the most economically important nation in the world, Jean-Claude Trichet, former president of the European Central Bank, told CNBC on Wednesday.

When asked about the federal government shutdown, Trichet said it "signals enormous difficulty for the democracy of the United States.

"I hope very, very much that a solution will be found out. I think it's essential, crucial, for the U.S. and very, very important for the global economy," he told "Squawk on the Street." "What would be totally absurd is that the debt ceiling would not be augmented in two weeks ... because there we are playing with the credibility of the United States."

For Europe to recover, both governing institutions and individual countries must "embark on very, very bold structural reforms, not only for more labor flexibility, which is overdue ... but also in the domains of food and services," Trichet said.

Without such reforms, the euro zone will not achieve the "single market" that was the ultimate goal of the European experiment, he said, adding that "a lot remains to be done."

Looking back at the financial crisis and its aftermath, Trichet said that early in the recession it would have been "very difficult" to imagine that growth and employment in developed economies wouldn't have recovered by now.

Continued unconventional measures from the world's central banks demonstrate that "the episode we are observing is a major problem in all advanced economies," he said, adding that Japan, the U.S., the United Kingdom and the euro zone must enact fundamental changes before central banks can successfully wind down their support.

Trichet told CNBC last month that Europe requires a banking union "as soon as possible" to supervise the financial system and help avoid government bailouts in the wake of bank failures.